Science’s Cult of Calculation

The editors of Scientific American regularly encounter perspectives on science and technology that we believe our readers would find thought-provoking, fascinating, debatable and challenging. The guest blog is a forum for such opinions. The views expressed belong to the author and are not necessarily shared by Scientific American.

Jag Bhalla is an entrepreneur and writer. His current project is Errors We Live By, a series of short exoteric essays exposing errors in the big ideas running our lives, details at www.errorsweliveby.comwww.errorsweliveby.com. His last book was I'm Not Hanging Noodles On Your Ears, a surreptitious science gift book from National Geographic Books, details at www.hangingnoodles.comwww.hangingnoodles.com. It explains his twitter handle @hangingnoodles Follow on Twitter @hangingnoodles.

E. O. Wilson says great scientists need be “no more than semiliterate” mathematically. He says: doing the math is often easier than generating ideas; the math is usually out-sourceable; we have more mathematicians than useful ideas; and science advances by better ideas which typically don’t come from mathematical reasoning.

Math-monks follow Galileo’s faith that “the Book of Nature is written in the language of mathematics.” They believe mathematical descriptions are the one-true-way, the best and most reliable kind of knowing. Plural-reasoners side with polymath Pascal who warned against over reliance on the “spirit of geometry,” which sees only the mathematically characterisable. Physics’ successes spread Galileo’s gospel so far that J.S. Mill thought sociology would become “social astronomy.” We live in the aftermath of Galileo’s triumph, where rational is often reduced to meaning what can be shown by the numbers.

Wilson claims upset modern math-monks as detailed here. But why haven’t their tools, honed for the inanimate world of physics, been as useful in biology or the social sciences? Here are some seed ideas on what physics and its classical-math methods (geometry, algebra, statistics etc) are good at, and what their limits show:

Physics is forgetful. It deals only with forces that are active now, not with what was happening before. Classical math similarly has no memory and had to be computer-extended to enable path dependent simulations and models. But programming isn’t just math, it adds other logic.

Physics prefers peripheral ifs. Like classic-math it isn’t good at conditionals. Its ifs are used to decide which equations apply; they can’t be used within the equations. But biological behavior is centrally structured by if-then logic.

Physics loves interactions between simple objects and stable forces. But the animate sciences play fundamentally different games: what A does depends on what B is doing. Imagine how complex Newton’s third law would be if for every action there was one of n possible reactions, depending on how each biological billiard ball felt that day? Game theory is young but it can’t be done with only classical-math.

Idolizing classical-math style reasoning is a legacy of physics’ past triumphs. But such conventional number-smithing leaves out or doesn’t deal well with the logic of life’s conditionally scripted variable path dependent responses. So parts of biology need extensions to classical-math thinking. Wilson and Pascal’s pluralist-reasoners know, over-reliance on conventional math can be like searching for lost keys only in the lit part of the parking lot.

In science, as in life, we see with our ideas. Mathematical ideas are powerful tools of reason and science. But not understanding their limits, limits what can be reliably built with them. Undervaluing non-mathematical thinking ignores useful tools. Why should we limit ourselves to what can be expressed or supported mathematically? Cyber-critic Evgeny Morozov worries about “numeric imagination” displacing “narrative imagination.” Wilson agrees saying “scientists should think like poets and work like accountants” see TEDMED video below.

About the Author: Jag Bhalla is an entrepreneur and writer. His current project is Errors We Live By, a series of short exoteric essays exposing errors in the big ideas running our lives, details at www.errorsweliveby.comwww.errorsweliveby.com. His last book was I'm Not Hanging Noodles On Your Ears, a surreptitious science gift book from National Geographic Books, details at www.hangingnoodles.comwww.hangingnoodles.com. It explains his twitter handle @hangingnoodles Follow on Twitter @hangingnoodles.

4 Comments

Wilson doesn’t entirely diss math, but simply says “advanced” math isn’t necessary for success in science — the debate then becomes over what does or doesn’t qualify as “advanced” math.
As far as any restricted efficacy of math in the biological and social sciences, the question is whether that results from inherent limitations of mathematics (forever), or is it just that biology and social science are still at such a primitive stage that applicable math algorithms haven’t been discovered yet?

Faraday did some rather great physics, but could not do math. He referred to himself as “amathematical” and quipped that “the only mathematical operation I ever performed was turning the crank of the calculator.

He learned about electromagnetism via direct experiments on the physical world.

Let me add the point that some of Einstein’s greatest contributions were not mathematical discoveries. Rather they were conceptual discoveries about how nature actually worked.

Once he had the correct conceptual natural philosophy, then he would subsequently develop the mathematical formalism that gave the concepts the rigor and predictive power by which the conceptual ideas could be further developed and scientifically tested.

That is how real science is done.

As Einstein put it: “Books on physics are full of complicated mathematical formulas, but thought and ideas are the beginning of every physical theory.”

To expand on this point, the term “social sciences” was presumptuous at birth, and its scholars have done precious little but add mathematics to their tools wherever possible, to earn the name “science.”

If you can’t predict from theory all but infallibly within the limits of observation available to you, you ain’t doing science, whether math is involved or not. What you’re doing may be valuable, but value doesn’t define science either.